Good morning Kat
This is a total bummer and a position many people find them selves in.
With any tile a tiny fracture can put a hairline crack in and this crack may not even show up until after the grouting process. Even my best setters here in Vancouver will leave a chip behind every now and then.
The fix is simple. Depending on your tile backer board and if there is no glass hardware in the way.
If you are new here on Terry's site you will have been spared the back and forth Jim and I have over backer boards. But if you have been reading for a while you might not be surprised than some people actually use drywall as a backer.
Do you recall the backer board used behind the tiles and waterproofing?
Some backer boards are made out of cement.
Some are made out of cement and recycled products.
Some are made out of fiberglass product.
Some are foam board.
And some are a gypsum based or drwall type product. The last two options the worst of the lot for a tile switch.
If however you have a stronger backer board like a cement board, wonder board, Super Panel or Hardi Board (Durock is another) the replacement tile can easly be banged out with a nasty old screwdriver and hammer. We typically use a grout saw to relieve the grout around the perimeter some and then bang the sucker out. Re set a new tile and grout.
Prying off a large tile over a sheet membrane is tricker. Here we use a grinder and do multiple saw cuts with a diamond blade and then chip the tile out. Being careful not to go through the mortar and cutting the waterproofing.
Prying off a large tile over a liquid membrane is as tricky and we use the same approach. But at patch on an accidentally damaged waterproofing is much easier with liquid sinc e there is no need for an overlap.
Can you post a picture of the tile in question?
Do you have any stone work left to do in the house? The reason I ask is that many of the stone installers are masters at the epoxy repair. Stone counters often need repairing and my guys here in Vancouver have at times blended three types of epoxies to make custum repairs.
Hope this helps.